The least count of a stop watch is 0.2 s, The time of 20 oscillations of a pendulum is measured to be 25s. The percentage error in the time period is

Options

A. `1.2%`
B. `0.8%`
C. `1.8%`
D. None of these

Explanation

To solve the problem of finding the percentage error in the time period of a pendulum based on the given data, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Least count of the stopwatch (Δt) = 0.2 seconds
- Total time for 20 oscillations (T) = 25 seconds

2. **Calculate the Time Period (T_p):**
- The time period (T_p) for one oscillation can be calculated using the formula:
\[ T_p = \frac{T}{n} \]
where \(n\) is the number of oscillations. Here, \(n = 20\).
- Substituting the values:
\[ T_p = \frac{25 \text{ s}}{20} = 1.25 \text{ s} \]

3. **Determine the Absolute Error in Time Period (ΔT_p):**
- The absolute error in the time period is the same as the least count of the stopwatch:
\[ ΔT_p = Δt = 0.2 \text{ s} \]

4. **Calculate the Percentage Error in Time Period:**
- The percentage error can be calculated using the formula:
\[ \text{Percentage Error} = \left( \frac{ΔT_p}{T_p} \right) \times 100 \]
- Substituting the values:
\[ \text{Percentage Error} = \left( \frac{0.2 \text{ s}}{1.25 \text{ s}} \right) \times 100 \]
- Calculating this gives:
\[ \text{Percentage Error} = \left( 0.16 \right) \times 100 = 16\% \]

### Final Answer:
The percentage error in the time period is **16%**.

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